Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
(i) 25
(ii) 37
(iii) 54
(iv) 71
(v) 96

To find: 

We have to find the square of the given numbers using column method and verify the results by finding the squares using the usual multiplication.

Solution: 

(i) Let $a=2$ and $b=5$

$a^2$$2ab$$b^2$
$2^2=4$$2\times2\times5=20$$5^2=25$

$4+2(carry)=6$

$20+2=22$

$(25)^2=25\times25$

$=625$

Hence verified.

(ii) Let $a=3$ and $b=7$

$a^2$$2ab$$b^2$
$3^2=9$$2\times3\times7=42$$7^2=49$

$9+4(carry)=13$

$42+4=46$

$(37)^2=37\times37$

$=1369$

Hence verified.

(iii) Let $a=5$ and $b=4$

$a^2$$2ab$$b^2$
$5^2=25$$2\times5\times4=40$$4^2=16$

$25+4(carry)=29$

$40+1=41$

$(54)^2=54\times54$

$=2916$ 

Hence verified.

(iv) Let $a=7$ and $b=1$

$a^2$$2ab$$b^2$
$7^2=49$$2\times7\times1=14$$1^2=1$

$49+1(carry)=50$

$14$

$(71)^2=71\times71$

$=5041$ 

Hence verified.

(v) Let $a=9$ and $b=6$

$a^2$$2ab$$b^2$
$9^2=81$$2\times9\times6=108$$6^2=36$

$81+11(carry)=92$

$108+3(carry)=111$

$(96)^2=96\times96$

$=9216$  

Hence verified.

Updated on: 10-Oct-2022

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